The Ohio State University Alumni Association

Hero image

Ten riddles that put your math skills to the test

Give your brain a workout with these fun math riddles from Ohio State Professor Jim Fowler, dubbed “the prof who is making calculus go viral” by Forbes.

Forbes magazine called Jim Fowler “the prof who is making calculus go viral.” Now, this assistant professor of mathematics — renowned for his knack for teaching via online courses, video and virtual reality — has a challenge for you: two handfuls of math riddles compiled especially for Ohio State Alumni Magazine readers. Pencils up.

1

How did I get here?

Yes, you should get back to 1. That this happens is known as the Collatz conjecture, but it has not been proven — yet.

2

It’s OK to cut corners

No, you can’t completely cover the chessboard. Each domino covers a light square and a dark square, but after removing opposite corners, there are different numbers of light and dark squares.

3

Give this a try

No whole number, when multiplied by itself, ends in a 3. In fact, the units digits of perfect squares are 0, 1, 4, 5, 6, 9.

4

OK, world traveler

Yes. Here’s how: Cut the Earth in half along a great circle through the first two cities; of the other three cities, two are on the same piece.

5

Power play

It’s the same as the number you started with. Bonus question: Does this work if fifth power is replaced by fourth power?

6

Party of 6 please

Yes. In addition to yourself, you’re friends (or strangers) with three of the other five people. Suppose it’s friends. Then if those three people are mutual strangers, you’ve found your three people. If not, one pair of your friends are friends with each other, and with you and that pair you’ve found your three. This is an example of Ramsey theory, a branch of mathematics that studies the conditions under which order must appear.

7

The chance of regifting

Among a large number of guests, this would happen about 37 percent of the time. Surprisingly, the probability is closer to 1/e as the number of guests gets larger.

8

A perfect power

25 is 5 times 5, and 27 is 3 times 3 times 3.

9

Nine, you’re a square

71 = 1 + 9 + 25 + 36

10

Awwwww, is that all?

The remainder is 1, 10 or 26. Are you surprised that there are only three possibilities?

About the author

Victoria Ellwood

Victoria Ellwood is a freelance writer in Columbus.